Multiply the following complex numbers: $({-5+5i}) \cdot ({-2+2i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-5+5i}) \cdot ({-2+2i}) = $ $ ({-5} \cdot {-2}) + ({-5} \cdot {2}i) + ({5}i \cdot {-2}) + ({5}i \cdot {2}i) $ Then simplify the terms: $ (10) + (-10i) + (-10i) + (10 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 10 + (-10 - 10)i + 10i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 10 + (-10 - 10)i - 10 $ The result is simplified: $ (10 - 10) + (-20i) = -20i $